A Met Office yellow 'be prepared' alert for snow and ice in the county came into force at 6am and ends at 6pm.
Three roads which had to be closed have now re-opened.
The A57 Snake Pass, A537 Cat and Fiddle and A53 Leek Road are all now ‘passable with care’, according to Derbyshire County Council.
The A6024 Holme Moss remains closed and is not expected to re-open today.
The snow has now stopped and turned to rain as temperatures rise slightly.
According to the emergency services, there have been several crashes across the county and people are being urged to take extra care if they have to travel.